Representative Curves for Longitudinal Data via Regression Trees

Abstract

Simple superposition of individual curves, as arise in longitudinal studies, makes the detection of structure difficult due to clutter. This is especially true when the number of curves is large, but can even be exhibited in moderate sample settings when variability is high. Both Jones and Rice and Diggle, Liang, and Zeger proposed methods for identifying representative curves from a large collection that display the form and extent of variation of the curves. Here we propose the use of tree-structured regression, as adapted to longitudinal data, for this purpose. Properties of each method are described. A re-examination of atmospheric ozone data, analyzed by Jones and Rice, is also presented.

Key Words:

• Graphics
• Growth curves
• Principal components
• Tree-structured regression